civonamzuk

A = 1/2[3(3 * sin45º)]

https://web2.0calc.com/questions/geometry_10279#r2

AC = 8

∠CAE = 45º

∠C = arctan(6/8)

∠AEC = 180 - (∠CAE + ∠C)

CE = (sinCAE * 8) / sinAEC

EF = sinC * CE

You can do the rest. 

Let's fix up this question first.

~~~~~~~~~~~~~~~~~~~~~~~~~

Arturo had some marbles. 1/4 of the marbles were blue, 3/12 of the marbles were red, and the rest were yellow. There were 14 more yellow marbles than red marbles. How many marbles did Arturo have altogether?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Now we can solve this problem.

       1       :        1         :        2

1/4 blue      3/12 red        yellow

     x      +       x       =        x + 14 

x = 14

Arturo had 56 marbles. 

x - 41 / x - 51 = 3 / 1

3(x - 51) = x - 41

x = 56

Peter and Blake had $56 each.

A cylinder and a cone have the same volume. The cylinder has radius x and height y. The cone has a radius of 1/3x. Find the height of the cone in terms of y.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The height of a cylinder     y = V / r²pi

The height of a cone        (n)y = 3V / (r / 3)²pi

                                      (n)y / y = [3V / (r / 3)²pi] / (V / r²pi) = 27

The height of a cone = 27y

The length of a side is:    (7√3) / cos30º = 14

The ratio of the number of marbles Kaden, Adam, and John gave away was 2:4:9. The number of marbles Kaden gave away was 2 fewer than the number of marbles he had left. Adam had 1/2 as many marbles left as John. Kaden had 1/2 as many marbles left as Adam. They had a total of 56 marbles left. How many marbles did John give away?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

John gave away 27 marbles!

All marbles that are given away    6 + 12 + 27 = 45

All marbles left     8 + 16 + 32 = 56

0.75 = all the above 

Andy and Marcus each bought the same storybook and both of them started reading their books on the same day. Marcus read 3 fewer pages than Andy each day. Marcus took 80 days to finish his storybook while Andy took 30 days fewer than him. Find the number of pages in the storybook.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Marcus => 80(x - 3)               Andy => 30x

80(x - 3) = 30x

x = 4.8       (The number of pages Andy read each day.)

Number of pages in a book=>   4.8 * 30 = 144